Rule of three (mathematics)

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In mathematics, the rule of three is the method of finding the fourth term of a mathematical proportion when three terms are known. It is based on the principle that the product of the first and fourth terms (called the extremes) is equal to the product of the second and third terms (called the means).

In order to solve problems such as "If a car driving at a constant speed can in 3 hours drive 240 miles, how far can the car drive in 7 hours?"

The equation is set up as "3 is to 240 as 7 is to 'X'" or:

$a\ \hat =\ b$

$c\ \hat =\ x$

a, b and c are the values given, in this case 3, 240, and 7, and x is the value to be determined. It is important the quotient values are in the same unit system.

One now calculates the diagonal values, that is, c and b are multiplied and then divided by a. The result is then x.

$x = {c \cdot b \over a}$

For the example given, the car will drive for 560 miles in 7 hours. The speed of the car can also be determined, this is 80 mph. Another method would be to calculate the proportion and use it; that is, $b \over a$ and then multiplying by c to get x, which is mathematically equivalent to $x = {c \cdot b \over a}$